Finite Group Databasebeta

← C24×C17×C53 #72192591

Subgroups — C24×C17×C53 #72192591

Order 14416.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C17×C53C2115yesmaximal, direct product factor
2C22×C17×C53C22135yesdirect product factor
3C2×C17×C53C23115yesdirect product factor
4C17×C53C2411yescharacteristic, direct product factor, Hall
5C24×C53C1711yesmaximal, characteristic, direct product factor, Hall
6C23×C53C2×C17115yesdirect product factor
7C24×C17C5311yesmaximal, characteristic, direct product factor, Hall
8C22×C53C22×C17135yesdirect product factor
9C23×C17C2×C53115yesdirect product factor
10C2×C53C23×C17115yesdirect product factor
11C22×C17C22×C53135yesdirect product factor
12C53C24×C1711yescharacteristic, direct product factor, Sylow
13C2×C17C23×C53115yesdirect product factor
14C17C24×C5311yescharacteristic, direct product factor, Sylow
15C24C17×C5311yescharacteristic, direct product factor, Sylow
16C23C2×C17×C53115yesdirect product factor
17C22C22×C17×C53135yesdirect product factor
18C2C23×C17×C53115yesdirect product factor
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C23×C17×C53C2direct (N × H)
2. C22×C17×C53C22direct (N × H)
3. C2×C17×C53C23direct (N × H)
4. C17×C53C24direct (N × H)
5. C24×C53C17direct (N × H)
6. C23×C53C2×C17direct (N × H)
7. C24×C17C53direct (N × H)
8. C22×C53C22×C17direct (N × H)
9. C23×C17C2×C53direct (N × H)
10. C2×C53C23×C17direct (N × H)
11. C22×C17C22×C53direct (N × H)
12. C53C24×C17direct (N × H)
13. C2×C17C23×C53direct (N × H)
14. C17C24×C53direct (N × H)
15. C24C17×C53direct (N × H)
16. C23C2×C17×C53direct (N × H)
17. C22C22×C17×C53direct (N × H)
18. C2C23×C17×C53direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×C17×C532
C24×C5317
C24×C1753